How much overfitting is acceptable?
Validation results will almost never be as good as training results; that's just natural. As long as they are not too different, you should be fine. What &quot;too different&quot; means depends on the particular data set and model you're using.
If you plot the curves for varying parameter values, when the training error keeps going down but the validation error starts going up again, that's when you know there is overfitting. In your second graph, after 14 epochs, we might see the start of overfitting. If you continue this until 20 epochs or so, it should be even more clear. I would guess that 12 is probably a good value for the number of epochs for that problem.
In the first graph, we don't see that happening yet. The model might not be well-suited (the gap between training and validation results is a bit larger)  but that can also be because of too little data, or other factors. Perhaps that's just the best you can do; there might be noise in the data or something.